Currency per U.S. $ Australia dollar 1.2377 6-months forward 1.2356 Japan Yen 10

Question

Currency per U.S. $ Australia dollar 1.2377 6-months forward 1.2356 Japan Yen 100.3300 6-months forward 100.0500 U.K. Pound .6792 6-months forward .6781 Suppose interest rate parity holds, and the current risk-free rate in the United States is 5 percent per six months.

Use the approximate interest rate parity equation to answer the following questions.

Requirement 1: What must the six-month risk-free rate be in Australia? (Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Risk-free rate %

Requirement 2: What must the six-month risk-free rate be in Japan? (Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Risk-free rate %

Requirement 3: What must the six-month risk-free rate be in Great Britain? (Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Risk-free rate %

Explanation / Answer

Answer:

The approximate interest rate parity equation is:

Ft = S0 * [1+ (RFC - RUS)]t

where, t = No. of days

Ft = Forward rate for number of days

Here, t = 6 months. Hence, Ft = 180 - day forward rate (6 months * 30 days in each month)

S0 = Current spot rate expressed in units of foreign currency per one U.S. dollar

RFC = Foreign country nominal risk free interest rate

RUS = U.S. current risk free rate

To find out RFC , we will rearrange the approximate interest rate parity equation. The equation we will use is:

RFC = [(Ft - S0 )/S0] + RUS

Using this relationship, we find:

1) Australia : RFC = [($1.2356 - $1.2377)/$1.2377] + 0.05

RFC = (- 0.0021/1.2377) + 0.05

RFC = 0.04830 or 4.83%

2) Japan: RFC = [(Yen 100.0500 - Yen 100.3300)/Yen100.3300] + 0.05

RFC = (-0.2800 / 100.3300) + 0.05

RFC = 0.04720 or 4.72%

3) Great Britain : RFC = [(Pound 0.6781 - pound 0.6792)/ pound 0.6792] + 0.05

RFC = (-0.0011/0.6792) + 0.05

RFC = 0.04838 or 4.84%

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